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Math Expert V
Joined: 02 Sep 2009
Posts: 58401
If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 53% (01:49) correct 47% (01:56) wrong based on 79 sessions

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If a = c*10^b and a and b are integers, what is the value of b?

(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.
(2) 1 < b < 4

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Joined: 25 Feb 2013
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If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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Bunuel wrote:
If a = c*10^b and a and b are integers, what is the value of b?

(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.
(2) 1 < b < 4

Statement 1: $$c=0.xyz$$, where $$x,y,z$$ are digits in tenths, hundredths, and thousandths places but nothing mentioned about $$a$$ or $$b$$. Hence $$insufficient$$

Statement 2: $$b$$ can be $$2$$ or $$3$$. Hence insufficient

Combining 1 & 2. $$a = c*10^b$$,

or $$a= 0.xyz*10^b$$ we know that $$a$$ is an integer, hence $$b=3$$ because if $$b=2$$ then $$a=xy.z$$ which is not an integer. Hence sufficient

Option C

Originally posted by niks18 on 03 Oct 2017, 02:20.
Last edited by niks18 on 15 Oct 2017, 02:00, edited 2 times in total.
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GMAT 1: 730 Q50 V38 If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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If $$a = c*10^b$$and a and b are integers, what is the value of b?

(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.
=> This tells us that c is a 3 digit decimal number => c = 0.pqr ( p,q,and r are single digit integers)

to make 'a' as an integer 'c' need to be multiplied by 1000 => minimum value of a => $$a = c*10^3$$
Here as we don't know value of a => b can take any value greater or equal to 3 => $$b\geq{3}$$
Insufficient

(2) 1 < b < 4
as b is an integer => b = 2 or 3
Insufficient

1+2

=>by statement 1=> $$b\geq{3}$$
by statement 2 => b = 2 or 3
=> b=3

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Re: If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.

How come you can deduce that "C" is a decimal digit ?
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Re: If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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kunalsinghNS wrote:
(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.

How come you can deduce that "C" is a decimal digit ?

Hi kunalsinghNS

it is mentioned in the statement that ONLY tenths, hundredths, and thousandths places have non zero digits
So $$c=0.234$$ or $$c=10.897$$. In either case if you multiply $$c$$ by $$10^3$$, then it will become an integer
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GMAT 1: 730 Q50 V38 If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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kunalsinghNS wrote:
(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.

How come you can deduce that "C" is a decimal digit ?

Please refer attached figure and below mentioned line, it might help.

c has nonzero digits in only the tenths, hundredths, and thousandths places.
Attachments Number.jpg [ 16.72 KiB | Viewed 1057 times ]

Manager  B
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Re: If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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Thank you for the explanation niks18 and Nikkb
Senior Manager  G
Joined: 13 Feb 2018
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GMAT 1: 640 Q48 V28 Re: If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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It will help if you catch the difference
tens-tenth
hundreds - hundredth
thousands - thousandth
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Re: If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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If a = c*10^b and a and b are integers, what is the value of b?

(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.
(2) 1 < b < 4

In statement 1 value of c can be variable of 10 but no such description about the b while in statement 2 value of b is between 1 to 4 so on combining both statements we get value of a Re: If a = c*10^b and a and b are integers, what is the value of b?   [#permalink] 11 Jul 2019, 00:31
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